Analytic Extension Formulas and their Applications

by S. Saitoh (Editor), N. Hayashi (Editor), M. Yamamoto (Editor)

Overview

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.
Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.

Product Details

ISBN-13:	9781441948540
Publisher:	Springer US
Publication date:	12/07/2010
Series:	International Society for Analysis, Applications and Computation , #9
Edition description:	Softcover reprint of hardcover 1st ed. 2001
Pages:	288
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. Extending holomorphic functions from subvarieties.- 2. Representations of analytic functions on typical domains in terms of local values and truncation error estimates.- 3. Uniqueness in determining damping coefficients in hyperbolic equations.- 4. Analytic continuation of Cauchy and exponential transforms.- 5. Analytic function spaces and their applications to nonlinear evolution equations.- 6. A sampling principle associated with Saitoh’s fundamental theory of linear transformations.- 7. The enclosure method and its applications.- 8. On analytic properties of a multiple L-function.- 9. Multi-dimensional inverse scattering theory.- 10. Holomorphic spaces related to orthogonal polynomials and analytic continuation of functions.- 11. Extension and division on complex manifolds.- 12. Analytic extension formulas, integral transforms and reproducing kernels.- 13. Analytic continuation beyond the ideal boundary.- 14. Justification of a formal derivation of the Euler-Maclaurin summation formula.- 15. Extension of Löwner-Heinz inequality via analytic continuation.- 16. The Calogero-Moser model, the Calogero model and analytic extension.

Editorial Reviews

Sixteen papers from two meetings on analytic extensions, one held under the auspices of the International Society for Analysis, its Applications and Computation (second international congress, Fukuoka Institute of Technology, August 1999) and the other a research session at Kyoto U. (January 2000). The papers cover several fields in analysis, including analytic extension formulas, integral transforms, reproducing kernel, operator inequalities, partial differential equations, and inverse problems. The contributors are mathematicians and engineers based in Japan, Russia, the US, and Europe. There is no subject index. Annotation c. Book News, Inc., Portland, OR (booknews.com)